Webster's Method for Signal Timing
Webster's method, developed in 1958 and still the basis of the HCM's isolated intersection signal timing procedure, determines the cycle length that minimizes total vehicle delay at a pre-timed traffic signal. It reduces a complex queueing problem to a small set of inputs: lost time per phase and the critical flow ratio for each signal phase.
Critical Flow Ratios and Capacity
Each phase's critical flow ratio, Yᵢ = vᵢ/sᵢ, is the demand volume divided by the saturation flow rate of the critical lane group serving that phase — typically 1,600 to 1,900 vehicles per hour of green (vphg) per lane, adjusted downward for narrow lanes, grades, and turning movements. The sum of all phases' critical ratios, ΣYᵢ, is a direct measure of how close the intersection is to capacity: values well below 1.0 indicate reserve capacity, values approaching 1.0 indicate the intersection is nearing saturation, and values at or above 1.0 mean it is already over capacity and no cycle length can serve the demand without queuing beyond one cycle.
Optimal Cycle Length
Webster's formula, C₀ = (1.5L + 5)/(1 − ΣYᵢ), computes the theoretical delay-minimizing cycle length from total lost time (L, typically 3–5 seconds per phase) and ΣYᵢ. Each phase then receives a share of the remaining "effective green" time proportional to its own Yᵢ relative to the total. In practice, agencies round the computed cycle to the nearest 5 or 10 seconds for coordination with adjacent signals along a corridor.
Limitations — Isolated vs. Coordinated Signals
Webster's method assumes an isolated, pre-timed intersection with random, uncoordinated arrivals — an assumption that rarely holds on a signalized arterial where adjacent signals are coordinated to create progression bands. Actuated signals, which extend or truncate green time based on real-time detector calls, and coordinated systems, which subordinate individual intersection optimality to corridor-wide progression, both require dedicated HCM procedures and engineering judgment well beyond Webster's original single-intersection formula. Use this calculator for preliminary estimates and isolated intersections only.
What if ΣYᵢ comes out at or above 1.0?
The intersection is at or beyond capacity for the given lane configuration and volumes — no cycle length can serve that demand without a growing queue. The fix requires added capacity or demand reduction, not a longer cycle.
Why does the formula add 5 seconds to 1.5×L in the numerator?
Webster derived this constant empirically to minimize total intersection delay across a wide range of tested conditions — it isn't an arbitrary buffer but part of the calibrated delay-minimization formula and shouldn't be adjusted independently.
How is saturation flow rate (s) actually determined for my intersection?
The HCM base saturation flow rate (1,700–1,900 vphg per lane) is adjusted downward using factors for lane width, heavy vehicles, grade, parking, and turning movements specific to each lane group. Field-measured values are more reliable than base values alone.
Does this calculator size the yellow and all-red clearance intervals too?
No — Webster's method computes cycle length and green splits only. Yellow change and red clearance intervals are calculated separately using ITE's kinematic formula and added to the green times this calculator produces.
Why might my agency's actual signal timing differ from Webster's optimal cycle?
Coordination with adjacent signals along a corridor often overrides isolated-intersection optimization — agencies commonly use a common cycle length across coordinated signals to maintain progression bands, even where Webster's formula would suggest a shorter cycle.